Devices and methods disclosed herein relate generally to data accuracy, and more specifically, to computing uncertainty for gridded data sets, for example, for historical gridded bathymetry data.
Estimates of uncertainty are becoming a requirement of oceanographic and acoustic models that use bathymetry. Further, bathymetry fusion algorithms that fuse disparate data sets into a single bathymetry surface can require uncertainty estimates of the input data. Still further, International Hydrographic Organization (IHO) standards prescribe that uncertainty be specified for all hydrographic and bathymetric products, with differing level of uncertainty tolerances depending on safety requirements. Ultimately, uncertainty in the bathymetry layer can be used for navigation safety for surface ships and submarine operations. Jakobsson et al., On the effect of random errors in gridded bathymetric compilations, Journal of Geophysical Research-Solid Earth, 107: Article 2358, 2002, estimate error on historic data sets based on Monte Carlo simulations where the two-dimensional position of the original data points, the soundings, are randomly perturbed using a normally distributed random number generator (RNG) illustrated in FIG. 1 (PRIOR ART), showing the established Monte Carlo procedure 100 as given originally by Jakobsson. FIG. 2 (PRIOR ART) shows a revised established Monte Carlo procedure 150, revised to match the notation and flow chart conventions used herein, where the number of soundings is J, the number of surveys is K, the horizontal and vertical uncertainties of the Kth survey are HK and VK, the number of Monte Carlo simulations is N, and each loop is denoted by. For the Kth survey, the RNG perturbs the position data ˜(0,VK2). The notation ˜(0,VK2) means that the quantity follows a normal, or Gaussian, probability distribution with mean 0 and variance VK2. If the output grids have I grid points, the gridded bathymetry surface is constructed 151 from a conventional minimum curvature spline interpolator for each nth iteration, resulting in N different interpolated bathymetry surfaces 153. The gridded uncertainty estimate is the standard deviation 155 of the N surfaces. Navigation error and the bottom slope can predominantly influence the bathymetric uncertainty estimated from this method. This procedure can be computationally intensive and requires the use of original soundings data.
What are needed are a system and method that can estimate uncertainty in the interpolation/extrapolation of bathymetry data. What are further needed are a system and method that provide a statistically rigorous means for estimation of uncertainty for areas of the seafloor not covered by dedicated surveys or that fall in between point measurement locations, and that are computationally efficient and do not require the use of original soundings data.